|Title:||A direct solver for the least‐squares problem arising from GMRES(k)||Authors:||Galán, Manuel J.
|UNESCO Clasification:||1206 Análisis numérico||Keywords:||Algorithm||Issue Date:||1994||Journal:||Communications in Numerical Methods in Engineering||Abstract:||This is a study about one of the core questions in the GMRES(k) method regarding the obtaining of vector yk for the least‐squares problem, argminy |Hky ‐ β(n)e1|2 (see Saad and Schultz1). We propose a simple but efficient approach to the resolution of this problem and a low cost computation of the residual and the residual norm, including both in a complete and detailed FGMRES(k) algorithm. The whole algorithm of minimization only involves two backward substitutions with triangular matrices and a dot product. The residual and the residual norm are computed, making use of results in the least‐squares problem.||URI:||http://hdl.handle.net/10553/47213||ISSN:||1069-8299||DOI:||10.1002/cnm.1640100909||Source:||Communications In Numerical Methods In Engineering[ISSN 1069-8299],v. 10 (9), p. 743-749, (Septiembre 1994)|
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